To find out how many times larger the volume of the saltwater tank is compared to the volume of the freshwater tank, we first need to calculate the volume of each tank.
The volume \( V \) of a cube can be calculated using the formula:
\[ V = \text{side length}^3 \]
For the freshwater tank:
- Side length = 15 cm
\[ V_{\text{freshwater}} = 15^3 = 15 \times 15 \times 15 = 3375 \text{ cm}^3 \]
For the saltwater tank:
- Side length = 45 cm
\[ V_{\text{saltwater}} = 45^3 = 45 \times 45 \times 45 = 91125 \text{ cm}^3 \]
Now, to find out how many times larger the saltwater tank is compared to the freshwater tank, we divide the volume of the saltwater tank by the volume of the freshwater tank:
\[ \text{Ratio} = \frac{V_{\text{saltwater}}}{V_{\text{freshwater}}} = \frac{91125}{3375} \]
Calculating the above gives:
\[ \frac{91125}{3375} = 27 \]
Therefore, the saltwater tank is 27 times larger than the freshwater tank. The answer is:
27